Mutual Information of MIMO-OFDM Integrated Sensing and Communication System in Space–Time–Frequency Domains

With the continuous development of emerging applications such as autonomous driving, intelligent robotics, and low-altitude economy in the 6th generation (6G) wireless systems, the research on integrated sensing and communication (ISAC) is also advancing. The ISAC performance metrics are of great significance in the optimization of the ISAC system. In this paper, mutual information (MI) is applied to evaluate the performance of sensing and communication. Specifically, the closed-form expressions of communication and sensing MIs for uplink and downlink multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) ISAC system in space-time-frequency domains are derived, which address the multi-domain correlation problem. Besides, the equivalence between minimum mean square error (MMSE) and sensing MI is proved. The optimal waveform structures under average power constraints are derived with the criteria including maximization of the sensing MI, minimization of the sensing MMSE, and maximization of the weighted sum of communication and sensing MIs for downlink and uplink ISAC systems. The proposed waveform optimization schemes are verified by numerical results, considering mutual interference between sensing and communication, demonstrating the improvements in ISAC performance based on the derived MIs in space-time-frequency domains. This paper proves the capability of MI as a unified metric of ISAC, establishing the bridge between communication information theory and sensing estimation theory.